The Frank copula
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The Frank copula is a copula that is sometimes used
in the modelling of codependency. It is an Archimedean copula,
and exchangeable.
Copula name

Frank copula

Common notation


Parameters


Domain


Copula

Or if we use the limit which
the independence
copula

Kendall’s rank
correlation coefficient (for bivariate case)

where is
the Debye function defined as:

Coefficient of upper
tail dependence,


Coefficient of lower
tail dependence,


Archimedean generator
function,

Or if we use the limit which
is taken as

Other comments

If we obtain the independence copula.
The Frank copula (like the Clayton copula) is a comprehensive
copula in that it interpolates between a lower limit of the countermonotonicity
copula () and an upper limit of the comonotonicity
copula ().

Nematrian web functions
Functions relating to the above distribution may be accessed
via the Nematrian
web function library by using a DistributionName of “Frank Copula”.
For details of other supported probability distributions see here.
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